On the generation of coastline-following grids for ocean models—trade-off between orthogonality and alignment to coastlines

Abstract

Regional ocean models usually utilize orthogonal curvilinear grids that are fit to the coastline of the modeled regions. While the orthogonality of the grid is required from the perspective of the numerical algorithms, the alignment to the irregular coastlines improves the characterization of the land-sea distribution and the ocean simulation. In this article, we carry out fractal analysis of two representative coastal regions and discuss the trade-offs between the orthogonality and coastline alignment during the grid generation of these regions. A new grid generation method based on Schwarz-Christoffel conformal mappings is proposed, with automatic coastal boundary retrieval algorithm that generates resolution dependent boundary for grid generation and alleviates the human efforts involved in traditional methods. We show that for the southeastern Pacific region, the coastline is smooth with low fractal dimension and there exists effective trade-off with a coastline boundary that Center of Earth System Sciences, Tsinghua University, Beijing, 100084, China adjusts to the desired grid resolution. On the contrary, there is no effective trade-off for southeast China seas where the coastline is of higher fractal dimension, and a coarser coastline boundary is recommended for better orthogonality with little loss in coastline alignment. Further numerical study of coastal trapped Kelvin waves for the typical regions demonstrate that the new coastline-fitting grids achieve smaller error in numerical dispersion and higher accuracy. Through analysis, we conclude that for grid generation for regional ocean modeling, modelers should bring into consideration of the multi-scale fractal characteristics of the coastline.

Analysis of Coastal Zone Data of Northern Yantai Collected by Remote Sensing from 1990 to 2018

“…In this study, the fractal dimension of the coastline is calculated by the grid method [29]. The basic principle of the grid method is to use square grids of different lengths to cover the measured coastline continuously and with no overlap.…”

Synthesizing nuclear power plant fouling with fractal characteristics enables an in-depth study of concerned nuclear safety issues

“…10 , 14 To study the wick boiling heat transfer and boron hideout within the CRUD depositions, overall properties of CRUD such as density, average pore sizes, average porosity, and average heat conductivity are insufficient. Based on statistical self-similarity, which means the local structure is similar to the whole, fractals or fractalline shapes have been proven to be able to better describe complex materials in nature and engineering, 15 including ocean coastlines 16 and sintered powder metallurgy components. 17 Also, the fouling deposits similar to CRUD have shown self-similarity of fractallines to a certain extent, such as salt crystallization deposition, 18 bio-membrane sludge, 19 and CaCO 3 deposition during boiling in heat exchangers.…”

A study on simulation the coastal flow in Soc Trang, Vietnam using the hydraulic model on curvilinear coordinates

“…Meanwhile, for the curvilinear coordinate system, because the land boundary is built according to shorelines, there has a velocity in the  direction. Therefore, simulation results in areas with complex bathymetry on curvilinear coordinates will be better than simulation on Cartesian coordinate system (Liu et al 2017;Morianou et al 2018;Yousefi and Veron 2020).…”